| 词汇 | example_english_complex-number |
| 释义 | Examples of complex numberThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. For these function the eigenvalue may be a complexnumber with a positive imaginary part. This does not totally remove the degeneracy since any solution when multiplied by a complexnumber with magnitude 1 will also satisfy this criterion. These normalized residues are a priori free complexnumber s depending on the considered pole of v (respectively b). Note that becomes a complexnumber in the case of instabilities. The constructor (:+) forms a complexnumber from its real and imaginary rectangular components. For this we need to think of r as a complexnumber. However, the tuple constructor that is used to pack the real and imaginary parts of the complexnumber forces a lazy context for its arguments. For every r there exist two real number solutions, or two complexnumber solutions or mixed solutions. Let us denote the argument of the complexnumber representing the amplitude of the initial perturbation amplitude. This vector can be represented as a complexnumber with unit magnitude. When one complexnumber and one real number solution are obtained, the real number gives the orientation change point at which the manipulator does not have continuing orientation. Its main feature is the 'inflation-subdivision' property: there is a complexnumber with > 1, such that multiplication by maps every tile into a union of tiles. For example, the type definition of a complexnumber is intended to be a strict one, but without language support it is not possible to indicate this. The example is a basic definition of a complexnumber: it defines the instance variables, and a method to initialize the object. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The path integral assigns to all these amplitudes "equal weight" but varying phase, or argument of the complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. So given a particular complexnumber one can ask how close is to being an algebraic number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Linear combinations combine multiplication and summation; they are sums in which each term has a multiplier, usually a real or complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Again, it is also possible to allow the geometric algebra to exit into the metrical real or complexnumber algebra if that is acceptable. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Moreover, a complexnumber is real if and only if it equals its conjugate. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The complexnumber can be identified with the point in the complex plane. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The real number is called the "real part" of the complexnumber; the real number is called the "imaginary part" of. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Using the polar form of the complexnumber in calculations may lead to a more intuitive interpretation of mathematical results. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Using the complex plane, we can treat as a complexnumber and circle as a set of complex numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Each stack level can contain any of the data types supported by the machine: real number, complexnumber, or vector. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. More generally a complexnumber is called a period if its real and imaginary parts are periods. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In fact, conic sedenions are isomorphic to complex octonions, i.e. octonions with complexnumber coefficients. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In mathematical terms, computes the principal value of the argument function applied to the complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is able to (almost) uniquely represent every complexnumber using only the digits 0, 1, 2, and 3. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since the complex numbers can be multiplied giving another complexnumber, this identification provides a means to multiply vectors. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A complexnumber is a quantity which can be written as the sum of a real number plus an imaginary number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Pairs of real and imaginary values form a complexnumber explained as real and imaginary parts. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Like the real number system, the complexnumber system is a field and is complete, but unlike the real numbers it is not ordered. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Non-integer powers of a complexnumber can have many different values, see failure of power and logarithm identities. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This line, called imaginary line, extends the number line to a complexnumber plane, with points representing complex numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It takes on every complexnumber excepting 0 as value; that is, 0 is a lacunary value of the exponential function. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This includes polynomials with real coefficients, since every real number is a complexnumber with zero imaginary part. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The scalar part of a biquaternion is then a complexnumber called a biscalar. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The structure factor is a complexnumber containing information relating to both the amplitude and phase of a wave. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A point in the complex plane can be represented by a complexnumber written in cartesian coordinates. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In interval analysis, a split complexnumber represents an interval with midpoint "x" and radius "y". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The differintegral parameter "q" may be any real number or complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Every complex linear space is also a real linear space (the latter "underlies" the former), since each real number is also a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The inner product between two state vectors is a complexnumber known as a probability amplitude. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Second, for any complexnumber, its additive inverse is also a complexnumber; and third, every nonzero complexnumber has a reciprocal complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This phase factor is itself a complexnumber of absolute value 1. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In this situation, a spinor is an ordinary complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A complexnumber whose second component is zero is associated with a real number: the complexnumber ("a", 0) is the real number "a". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Traditionally, is assumed to be a complexnumber, and subsequent sections of this article will comply with this usage. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The real part of a complexnumber is denoted by or; the imaginary part of a complexnumber is denoted by or. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, complexnumber representation is often more powerful for circuit analysis purposes. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Any nonrational power of a complexnumber has an infinite number of possible values because of the multi-valued nature of the complex logarithm (see below). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The rational power of a complexnumber must be the solution to an algebraic equation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A complexnumber is then in the spectrum if this property fails to hold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since is not hermitian, is, in general, a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Then, based on the limit definition, the complexnumber is supposed to be a good approximation to. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In particular, multiplication by a complexnumber of modulus 1 acts as a rotation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The signum of a given complexnumber "z" is the point on the unit circle of the complex plane that is nearest to "z". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The result of such an integration is called a period and is generally a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He called its elements motors, a term in parallel with the rotor action of an ordinary complexnumber taken from the circle group. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This is analogous to the fact that the exponential of a complexnumber is always nonzero. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The inner product of two vectors over the field of complex numbers is, in general, a complexnumber, and is sesquilinear instead of bilinear. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In other words, it is the complexnumber zero. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The complexnumber may either be expressed in rectangular form or, more commonly, in polar form. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These are essentially one-dimensional arrays used to store a real or complexnumber into each of their elements. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Often, the gain and phase elements of a channel's distortion are conveniently represented as a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Each of the subcarriers could be represented as a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For example, a programmer might create a new data type named complexnumber that would include real and imaginary parts. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. To convert between the rectangular and polar forms of a complexnumber, the conversion formulae given above can be used. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It can also be shown that a complexnumber is constructible if and only if its real and imaginary parts are constructible. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Substituting the complexnumber for the real on the second line makes the power have multiple possible values. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The failure of this identity is the basis for the problems with complexnumber powers detailed under failure of power and logarithm identities. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Exponentiating a real number to a complex power is formally a different operation from that for the corresponding complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since every nonzero complexnumber "z" has infinitely many logarithms, care is required to give such notation an unambiguous meaning. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In this expression, is the "real part" and is the "imaginary part" of the complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A purely imaginary number is a complexnumber whose real part is zero. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This formula can be used to compute the multiplicative inverse of a complexnumber if it is given in rectangular coordinates. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In other words, a complexnumber is represented by the vector ("a", "b") over the field of real numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. All quadratic equations will have two solutions in the complexnumber system, but need not have any in the real number system. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A matrix of this form is the matrix representation of a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The inner product of two vectors is a complexnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Only in dimension 2 can one construct entities where is replaced by an arbitrary complexnumber with magnitude 1, called anyons. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The magnitude of a complexnumber is the length of a straight line drawn from the origin to the point representing it. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. While analogous to ordinary orthogonality, particularly as it is known with ordinary complexnumber arithmetic, this condition is more subtle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The product of the bivector with a complexnumber on the unit circle is then called an "elliptical rotation". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. With the exception of zero, reciprocals of every real number are real, reciprocals of every rational number are rational, and reciprocals of every complexnumber are complex. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, because a complexnumber encodes not just a magnitude but also a direction in the complex plane, the phase difference between any two coefficients (states) represents a meaningful parameter. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The phase of the sinusoid varies with distance which results in the propagation constant being a complexnumber, the imaginary part being caused by the phase change. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A complexnumber whose real part is zero is said to be purely imaginary, whereas a complexnumber whose imaginary part is zero is a real number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Much computational work with complex numbers is involved. Other numeric types such as rationals and complex numbers are defined in libraries. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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